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Unformatted text preview: ME 375 Homework 2 : Solution October 6, 2009 Problem 1 Derive the equation of motion for the system shown, state any assumptions and draw the free body diagrams. Figure 1: Problem 1 1 Solution: The free body diagram is as follows: Figure 2: Problem 1FBD Assumptions: • The spring is massless and acts as an ideal spring • The cord only moves vertical • The two disks are both fixed together and only rotate around one point O • Assume no slipping Explanation of symbols used: • x : displacement of static equilibrium for the mass m • y : displacement of static equilibrium for the spring • θ : the angular displacement of the disk • F s : force • F k : spring force Solution: First, we know that the disk has an angular position θ . We can correlate this 2 to x and y as follows: x = Rθ y = 4 Rθ We have the following equations: For the mass m: m ¨ x = F s (1) For the disk J: J ¨ θ = RF s + 4 RF k (2) F k = ky (3) We also know the correlation between θ and x...
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This note was uploaded on 12/22/2011 for the course ME 375 taught by Professor Meckle during the Fall '10 term at Purdue.
 Fall '10
 Meckle

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